Open Access
Translator Disclaimer
2006 The mean field equation with critical parameter in a plane domain
Yilong Ni
Differential Integral Equations 19(12): 1333-1348 (2006).

Abstract

Consider the mean field equation with parameter $\lambda=8\pi$ in a bounded smooth domain $\Omega$. Denote by $E_{8\pi}(\Omega)$ the infimum of the associated functional $I_{8\pi}(\Omega)$. We prove that if $|\Omega|=\pi$, then $E_{8\pi}(\Omega)\ge E_{8\pi}(B_1)$ and equality holds if and only if $\Omega$ is a ball. We also give a sufficient condition for the existence of a minimizer for $I_{8\pi}(\Omega)$.

Citation

Download Citation

Yilong Ni. "The mean field equation with critical parameter in a plane domain." Differential Integral Equations 19 (12) 1333 - 1348, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35128
MathSciNet: MR2279331

Subjects:
Primary: 35J60
Secondary: 35J20 , 35J25 , 47J30 , 49J10

Rights: Copyright © 2006 Khayyam Publishing, Inc.

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.19 • No. 12 • 2006
Back to Top